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In this work, we consider loop-erased random walk (LERW) in three dimensions and give an asymptotic estimate on the one-point function for LERW and the non-intersection probability of LERW and… Click to show full abstract
In this work, we consider loop-erased random walk (LERW) in three dimensions and give an asymptotic estimate on the one-point function for LERW and the non-intersection probability of LERW and simple random walk in three dimensions for dyadic scales. These estimates will be crucial to the characterization of the convergence of LERW to its scaling limit in natural parametrization. As a step in the proof, we also obtain a coupling of two pairs of LERW and SRW with different starting points conditioned to avoid each other.
Keywords:
loop erased;
erased random;
three dimensions;
point function;
random walk;
one point
Journal Title: Electronic Journal of Probability
Year Published: 2019
Link to full text (if available)
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Journal Title: Electronic Journal of Probability
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!